Title:
Momentum-space resummation for transverse observables and the Higgs $p_\perp$ at N$^3$LL+NNLO

Abstract: We present an approach to the momentum-space resummation of global, recursive
infrared and collinear safe observables featuring kinematic zeros away from the
Sudakov limit. In the hadro-production of a generic colour singlet, we consider
the family of inclusive observables which do not depend on the rapidity of the
radiation, prime examples being the transverse momentum of the singlet, and
$\phi^*$ in Drell-Yan pair production. We derive a resummation formula valid up
to next-to-next-to-next-to-leading-logaritmic accuracy for the considered
observables. This formula reduces exactly to the customary resummation
performed in impact-parameter space in the known cases, and it also predicts
the correct power-behaved scaling of the cross section in the limit of small
value of the observable. We show how this formalism is efficiently implemented
by means of Monte Carlo techniques in a fully exclusive generator that allows
one to apply arbitrary cuts on the Born variables for any colour singlet, as
well as to automatically match the resummed results to fixed-order
calculations. As a phenomenological application, we present state-of-the-art
predictions for the Higgs-boson transverse-momentum spectrum at the LHC at
next-to-next-to-next-to-leading-logarithmic accuracy matched to fixed
next-to-next-to-leading order.